{
 "metadata": {
  "name": "",
  "signature": "sha256:7d28a26cdf8dcc7dff4df2bbf55b997dd5a7f551e135c7144a649ca564393e89"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import powerlaw\n",
      "print(powerlaw.__version__)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.3.1\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Set up "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab\n",
      "pylab.rcParams['xtick.major.pad']='8'\n",
      "pylab.rcParams['ytick.major.pad']='8'\n",
      "#pylab.rcParams['font.sans-serif']='Arial'\n",
      "\n",
      "from matplotlib import rc\n",
      "rc('font', family='sans-serif')\n",
      "rc('font', size=10.0)\n",
      "rc('text', usetex=False)\n",
      "\n",
      "\n",
      "from matplotlib.font_manager import FontProperties\n",
      "\n",
      "panel_label_font = FontProperties().copy()\n",
      "panel_label_font.set_weight(\"bold\")\n",
      "panel_label_font.set_size(12.0)\n",
      "panel_label_font.set_family(\"sans-serif\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from os import listdir\n",
      "files = listdir('.')\n",
      "if 'blackouts.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/blackouts.txt', 'blackouts.txt')\n",
      "if 'words.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/words.txt', 'words.txt')\n",
      "if 'worm.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/worm.txt', 'worm.txt')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import genfromtxt\n",
      "blackouts = genfromtxt('blackouts.txt')#/10**3\n",
      "words = genfromtxt('words.txt')\n",
      "worm = genfromtxt('worm.txt')\n",
      "worm = worm[worm>0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### Figure 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_basics(data, data_inst, fig, units):\n",
      "    from powerlaw import plot_pdf, Fit, pdf\n",
      "    annotate_coord = (-.4, .95)\n",
      "    ax1 = fig.add_subplot(n_graphs,n_data,data_inst)\n",
      "    x, y = pdf(data, linear_bins=True)\n",
      "    ind = y>0\n",
      "    y = y[ind]\n",
      "    x = x[:-1]\n",
      "    x = x[ind]\n",
      "    ax1.scatter(x, y, color='r', s=.5)\n",
      "    plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)\n",
      "    from pylab import setp\n",
      "    setp( ax1.get_xticklabels(), visible=False)\n",
      "\n",
      "    if data_inst==1:\n",
      "        ax1.annotate(\"A\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)\n",
      "\n",
      "    \n",
      "    from mpl_toolkits.axes_grid.inset_locator import inset_axes\n",
      "    ax1in = inset_axes(ax1, width = \"30%\", height = \"30%\", loc=3)\n",
      "    ax1in.hist(data, normed=True, color='b')\n",
      "    ax1in.set_xticks([])\n",
      "    ax1in.set_yticks([])\n",
      "\n",
      "    \n",
      "    ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)\n",
      "    plot_pdf(data, ax=ax2, color='b', linewidth=2)\n",
      "    fit = Fit(data, xmin=1, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')\n",
      "    p = fit.power_law.pdf()\n",
      "\n",
      "    ax2.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    fit = Fit(data, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')\n",
      "    from pylab import setp\n",
      "    setp( ax2.get_xticklabels(), visible=False)\n",
      "\n",
      "    if data_inst==1:\n",
      "       ax2.annotate(\"B\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)        \n",
      "       ax2.set_ylabel(u\"p(X)\")# (10^n)\")\n",
      "        \n",
      "    ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)\n",
      "    fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')\n",
      "    fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')\n",
      "    fit.plot_pdf(ax=ax3, color='b', linewidth=2)\n",
      "    \n",
      "    ax3.set_ylim(ax2.get_ylim())\n",
      "    ax3.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    if data_inst==1:\n",
      "        ax3.annotate(\"C\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)\n",
      "\n",
      "    ax3.set_xlabel(units)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_data = 3\n",
      "n_graphs = 4\n",
      "f = figure(figsize=(8,11))\n",
      "\n",
      "data = words\n",
      "data_inst = 1\n",
      "units = 'Word Frequency'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data_inst = 2\n",
      "#data = city\n",
      "#units = 'City Population'\n",
      "data = worm\n",
      "units = 'Neuron Connections'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data = blackouts\n",
      "data_inst = 3\n",
      "units = 'Population Affected\\nby Blackouts'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "f.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=.3, hspace=.2)\n",
      "figname = 'FigWorkflow'\n",
      "f.savefig(figname+'.eps', bbox_inches='tight')\n",
      "#f.savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/jeff/Desktop/powerlaw/powerlaw.py:687: RuntimeWarning: invalid value encountered in true_divide\n",
        "  )[1:]\n",
        "/Users/jeff/Desktop/powerlaw/powerlaw.py:687: RuntimeWarning: divide by zero encountered in true_divide\n",
        "  )[1:]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/jeff/anaconda3/lib/python3.4/site-packages/matplotlib/scale.py:100: RuntimeWarning: invalid value encountered in less_equal\n",
        "  a[a <= 0.0] = 1e-300\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HOOUU04MwcSLUrm0i0o0c6bZUlrJItNUKRYjAvfea908+efC69XgiUdOGi3jD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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10664b240>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blackouts = blackouts/10**3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Introduction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.sigma\n",
      "fit.distribution_compare('power_law', 'exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(12.754562675882063, 0.1522925560442657)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Basic Methods"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Visualization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### PDF Linear vs Logarithmic Bins"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "####\n",
      "figPDF = powerlaw.plot_pdf(data, color='b')\n",
      "powerlaw.plot_pdf(data, linear_bins=True, color='r', ax=figPDF)\n",
      "####\n",
      "figPDF.set_ylabel(\"p(X)\")\n",
      "figPDF.set_xlabel(r\"Word Frequency\")\n",
      "figname = 'FigPDF'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Kqa6tTFHXluSD//43bJB1wQUwYwZMnRpWEO7dOySXDh3Co8Pz54cZ8yLJ0la7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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11c96a080>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### Figure 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "figCCDF = fit.plot_pdf(color='b', linewidth=2)\n",
      "fit.power_law.plot_pdf(color='b', linestyle='--', ax=figCCDF)\n",
      "fit.plot_ccdf(color='r', linewidth=2, ax=figCCDF)\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=figCCDF)\n",
      "####\n",
      "figCCDF.set_ylabel(u\"p(X),  p(X\u2265x)\")\n",
      "figCCDF.set_xlabel(r\"Word Frequency\")\n",
      "\n",
      "figname = 'FigCCDF'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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F7Oru/RoW/k+uo64tyQsLF1bvtjhvHvTsCU89FWMlf/sbDBigcRPJH7nYj+RJ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\nycj/A0b3vmfzHztiAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11d2595f8>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "###\n",
      "x, y = fit.cdf()\n",
      "bin_edges, probability = fit.pdf()\n",
      "y = fit.lognormal.cdf(data=[300,350])\n",
      "y = fit.lognormal.pdf()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Identifying the Scaling Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D\n",
      "fit = powerlaw.Fit(data, xmin=1.0)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.37601504850371725"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=(250.0, 300.0))\n",
      "fit.fixed_xmin\n",
      "fit.given_xmin\n",
      "fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "272.0"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmax=10000.0)\n",
      "fit.xmax\n",
      "fit.fixed_xmax"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### Figure 3"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "#FigCCDFmax = powerlaw.plot_ccdf(data, linewidth=3)\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=None)\n",
      "FigCCDFmax = fit.plot_ccdf(color='b', label=r\"Empirical, no $x_{max}$\")\n",
      "fit.power_law.plot_ccdf(color='b', linestyle='--', ax=FigCCDFmax, label=r\"Fit, no $x_{max}$\")\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=1000)\n",
      "fit.plot_ccdf(color='r', label=r\"Empirical, $x_{max}=1000$\")\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=FigCCDFmax, label=r\"Fit, $x_{max}=1000$\")\n",
      "#x, y = powerlaw.ccdf(data, xmax=max(data))\n",
      "#fig1.plot(x,y)\n",
      "####\n",
      "#FigCCDFmax.set_ylabel(r\"$p(X\\geq x)$\")\n",
      "FigCCDFmax.set_ylabel(u\"p(X\u2265x)\")\n",
      "FigCCDFmax.set_xlabel(r\"Word Frequency\")\n",
      "handles, labels = FigCCDFmax.get_legend_handles_labels()\n",
      "leg = FigCCDFmax.legend(handles, labels, loc=3)\n",
      "leg.draw_frame(False)\n",
      "\n",
      "figname = 'FigCCDFmax'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/jeff/Desktop/powerlaw/powerlaw.py:1165: RuntimeWarning: divide by zero encountered in double_scalars\n",
        "  C = 1.0/C\n",
        "/Users/jeff/anaconda3/lib/python3.4/site-packages/scipy/optimize/optimize.py:461: RuntimeWarning: invalid value encountered in subtract\n",
        "  numpy.max(numpy.abs(fsim[0] - fsim[1:])) <= ftol):\n",
        "/Users/jeff/anaconda3/lib/python3.4/site-packages/scipy/optimize/optimize.py:461: RuntimeWarning: invalid value encountered in absolute\n",
        "  numpy.max(numpy.abs(fsim[0] - fsim[1:])) <= ftol):\n",
        "/Users/jeff/Desktop/powerlaw/powerlaw.py:808: RuntimeWarning: invalid value encountered in multiply\n",
        "  likelihoods = f*C\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AX3/ZdbaUchdwiaSgvbZEvPMoKBFh4cKFpKSkZD4GDBiQ+XpVt2HFpUuXPmu7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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11d8f10f0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Continuous vs. Discrete Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=230.0)\n",
      "fit.discrete\n",
      "fit = powerlaw.Fit(data, xmin=230.0, discrete=True)\n",
      "fit.discrete "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Comparing Candidate Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.power_law\n",
      "fit.power_law.alpha\n",
      "fit.power_law.parameter1\n",
      "fit.power_law.parameter1_name\n",
      "fit.lognormal.mu\n",
      "fit.lognormal.parameter1_name\n",
      "fit.lognormal.parameter2_name\n",
      "fit.lognormal.parameter3_name == None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "R, p = fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)\n",
      "print(R, p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "1.43148048496"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.152292556044\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Generative Mechanisms"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "(-0.070651754953475088, 0.70698857057674624)"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "(-0.070651754953475088, 0.70698857057674624)"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "print(fit.distribution_compare('power_law', 'exponential', normalized_ratio=True))\n",
      "print(fit.distribution_compare('power_law', 'truncated_power_law'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "(9.1359147187769985, 6.485614241379581e-20)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions\n",
        "(-0.91712308337398118, 0.17562683168695525)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(fit.distribution_compare('power_law', 'truncated_power_law'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Assuming nested distributions\n",
        "(-0.91712308337398118, 0.17562683168695525)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### Figure 4"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'lognormal')\n",
      "fig = fit.plot_ccdf(linewidth=3, label='Empirical Data')\n",
      "fit.power_law.plot_ccdf(ax=fig, color='r', linestyle='--', label='Power law fit')\n",
      "fit.lognormal.plot_ccdf(ax=fig, color='g', linestyle='--', label='Lognormal fit')\n",
      "####\n",
      "fig.set_ylabel(u\"p(X\u2265x)\")\n",
      "fig.set_xlabel(\"Word Frequency\")\n",
      "handles, labels = fig.get_legend_handles_labels()\n",
      "fig.legend(handles, labels, loc=3)\n",
      "\n",
      "figname = 'FigLognormal'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aejN3rvWk49WrtsaokqaJRCnlEaJvRnMs79e4XmkJCYHfrt8GW7ZYNU3++MOu\n8FQKNJEopTxC+LVwxn03jvD7R9HgQauyYnQ0LF0KFCgA06dbE3kpj6OJRCnlEUoXKs3m/pvZcnoz\n0qkf+EQDcOqUvXGp1OWKwXajA3TKhTd9573R1eirBH3UnZ92xcKSr2jfqiCrVyezsQhcu2b1WFSG\n6WB7GomIvvRl99dQpUEB/wJ82HgZRJaG5hM4cyaFjTduhPvvhwMH3BafulWu6ZF4079TZZx+F3KG\nP/6AcuUE/K4TWDQ/58+nsPFnn1m3B8+cCZ07uy1Gb6I9EqWU1ylVCnx9DcTk5++/YdgwiIpKZuOn\nn4ZVq6znTMaN0+qLNtBEopTyOL6+1sOJcT74AJo1g5Mnk/lA/frw00/WbcIvvOCWGJWTXtpSuYp+\nF3KOS5egf39YtszZVqzkdV78cBsvPt486Q/FxEB4uNWlUWnmtZe2jDG1jDHTjTFLjDED7I7HWwQE\nBHD8+PFk1w8aNIjJkydn6hihoaFUrFgxU/tQqkgR+M9/4O23wc/ParsYe5LRP/ai/YQZSV/B8vPT\nJGIDj00kInJARAYBPYA2dseTnapUqUKBAgUICAiIfw0dOjRbjhUREUGVKlWSXT99+nTGjRuXLceO\n4+PjQ6FChQgICCAwMJCWLVuyxLUuayo0UeUexljTyoeGQvnywIWaMHszay69RY2BL3PunPYuPUG2\nJxJjzGxjzDljzN5E7W2NMQeMMYeNMS8m89mOwGpgUXbHaSdjDKtWrSIiIiL+9cEHH7g9jtjYWLcd\n65dffiEiIoJDhw7Rr18/Bg8ezMsvv+y246ucpXFj2LMHWrUCLlaDWVv4Pc9/qTrkOUK/T2VwXQRe\neQXOnXNLrLmRO3okc4C2rg3GGF/gI0d7baCnMeYOY0wfY8y7xphyACKyUkTaAX3dEKdHmjt3Lo0b\nN+b555+nWLFiVK9ena1btzJnzhwqVapE6dKl+eKLL+K379evH88++yytW7emcOHCBAcHc9JlhNLH\nx4djjgIQ/fr1Y9CgQbRv355ChQqxadMm+vXrx/jx4+O3X758Offeey9FihShevXqrFu3DoA5c+ZQ\nu3ZtChcuTLVq1Zg5c2aG/n3Fixend+/eTJ8+nddee42LFy+muP8rV67Qrl07zp49S0BAAIULF+bP\nP/9k586dNGzYkGLFilGuXDmGDBlCdHR0hmJSnqlkSVizBiZOBHO1NMwN5Wr+wzz00nt8+GEKHxSx\nbvl64AG+YnjaAAAaMElEQVTYudNt8eYqbnoIrAqw12W5IbDWZXk0MDrRZ4KA94EZwPA0HkeSkly7\nc33WvtKrSpUqsmHDhiTXzZkzR/z8/GTu3LkSGxsr48aNk/Lly8vgwYMlKipK1q9fLwEBAXLlyhUR\nEenbt68EBATI5s2b5caNGzJs2DBp0qRJ/P6MMXL06NH4bYsUKSJbt24VEZHr169Lv379ZPz48SIi\nsmPHDilSpEh8bGfOnJEDBw6IiMjq1avl2LFjIiISFhYmBQoUkN27d4uIyKZNm6RChQrJ/ntdY4gT\nFRUlfn5+snbt2lT3Hxoaesv+d+3aJTt27JCbN2/K8ePH5Y477pD33nvvlmOn9l1QOcO6dSKBgSL4\nXhf8rgqInDyZyoeWLRMpWVLk00/dEmNO4vjvIsO/8X7uTVvxygOuM+icBhq4biAiYUC6K9q4FmkJ\nDg4mODg4QwG6k4jQuXNn/Pyc/3dMnTqVAQOsewxuu+02+va1OmXdu3dnypQpTJgwAX9/f1q1akWe\nPHk4cuQId999NwAdOnSgSZMmAEyZMoUiRYpw5swZypcvf8uxO3fuTMOGDQHImzdvgnWzZs1iwIAB\ntGjRAoBy5crFr2vfvn38+2bNmtG6dWs2b95M3bp1M3QO/P39CQwMJDw8PNX9SxJ3Xd13333x7ytX\nrswzzzxDWFgYw4YNy1A8yrO1bm1d6mrSJC8nTlhtJ05AikNnnTtDrVrQpQv8+KN1T3Gi73xuERoa\nmqUFAO1KJNk2QpYV1b7czRjD8uXLecj1xnkXpUuXjn+fP39+AEqWLJmgLTIyMn5fFVxKkxYsWJDi\nxYtz9uzZWxJJ4m0TO336NA8//HCS69asWcOkSZM4fPgwsbGxXL16NT6RZUR0dDTnz5+nePHiGdr/\noUOHeP7559m1axdXr14lJiaGevXqZTge5fkqVIA6dYhPJBcupOFDtWpZl7def926gJBLJf4je9Kk\nSZnan113bZ0BXP92qIjVK7FFVl/cspOIcMplutTIyEjCw8MT9CbSqmLFihw5cuSW9hs3btCtWzdG\njRrFX3/9xcWLF2nfvn2mns9Yvnw5fn5+1K9fP9X9JzUJ56BBg6hduzZHjhzh0qVLTJkyxa03Dyh7\nOP7uAKzHRwAioyI58HcKc28FBMCUKZAvX/YGl4vYlUh+AmoYY6oYY/IAjwMrsmLHObVme2Z+hBP7\n5ptv2LJlC1FRUYwfP56GDRsmeVkrqWPGXfMEGDBgAHPmzOG7774jNjaWM2fOcPDgQaKiooiKiiIw\nMBAfHx/WrFnD+vXr0xVj3DHCw8P58ssvGTx4MKNHj6ZYsWKp7r906dJcuHCBy5cvx7dFRkYSEBBA\ngQIFOHDgANOnT09XPCpnKlHC+T6uR7L99HaC5gax7dQ2e4LKQbKqZrs7bv9dCGwFahpjThlj+otI\nDDAYWAfsBxaLyG9ZcbyQkJAcMS6SWMeOHRM8R9KtWzfA+us78V/gKU2Lb4zhiSeeYNKkSZQoUYI9\ne/Ywf/78JD+b3L7j2h544AHmzJnDiBEjKFq0aPwdYAEBAXzwwQd0796d4sWLs3DhQjp16pTmGAHu\nueceAgICqFGjBrNnz+a9996L/0Kntv9atWrRs2dPqlatSvHixfnzzz+ZOnUqCxYsoHDhwjzzzDP0\n6NFDywfkAkn1SFpWbcncTnN5ZNEjrD2yNu07u3w515XyDQ4OzpJEolOkeJn+/ftToUIFXnnlFbtD\n8Ui56buQG0ybBv/3f9b7f/0LPvnEuW7rqa10WdyF99q8R886PVPf2fvvW7Xhv/4abrstW+L1VJmd\nIsWuwfZsE9cjyYm9kqygP5IqN0nq0lacRhUbsaHPBtp92Y4SBUrQulrrlHcWN5vEgw/CvHnWrWFe\nLqvu3tIeiZfp378/FStW1KfEk5Gbvgu5wbffOn/vH3rIqnOV2OnLpyldsDT+vv5p22lYGPTsCUOG\nwOjR1jwtXi6zPRJNJCpX0e+Cd9m92yqQCHDnnbB3bxb97p8+DY8+CgMHwgDvnzPWa2f/zaiceteW\nUir9AgOd73/91frtd8yykzkVKlg9kz59smBnniur7trSHonKVfS74F1EIDgYvv/e2VapEixcCI0a\nJf+5f67/g7+PPwXzFMz2GHMC7ZEopXItY2DdOhg82Nl28qRVTfHVV5Ovujvjpxm0mteK8Gvh7gnU\ny2mPROUq+l3wXv/9Lzz1VMJLWy1aWDdglS2bcNtYieWF9S+w/th61vVeR7mA9M/84E20R5KIjpEo\nlTt17gw//2zVLomzcSPccw+sTfRcoo/xYWrrqfSq04sms5twJPzWqYByg6waI3HLNPLuepHBaeRV\nyoKCguSzzz7L1mN8/fXXUqFCBQkICJA9e/bInXfeKWFhYVl+HP0ueL/oaJFx40SMSTgL3gsviNy4\ncev2M3+aKWWnlpVj4cfcH6yHIJPTyHtdjyQnci21W6ZMGfr378+VK1fsDiteUlOpZLWRI0cybdo0\nLl++zL333su+ffto1qwZYPUy+3j53TMq6/j5WQURN2yAMmWc7W+9BU2bgqOuW7yB9w9kafelVCpS\nyb2BehFNJB7AtdTu7t27+emnn5g8ebItsdgxY66IcPLkSWrXru32Yyvv9dBD8L//Qbt2zradO6Fu\nXVi8OOG2jSo2wtfH170BehGvSyQ5fYykXLlytG3bln379gGwYsUK7rzzTooVK0bz5s05cMCaHnvO\nnDk88sgj8Z+rUaMG3bt3j1+uWLEiv/zyCwAHDhygVatWlChRglq1avHVV1/Fb5e43G5q5+7o0aM8\n9NBDBAYGUrJkSXr37s2lS5fSHVOcGzduEBAQwM2bN7nnnnuoUaMGYPXSNm7cyNq1a3nttddYvHgx\nAQEBGS6cpXKnUqVg1SqYOtXqqYA1N2OPHvDMM7lujsZb6BiJF42RuJbaPXnypNx5550yYcIEOXjw\noBQsWFA2bNggMTEx8uabb0r16tUlOjpajh49KkWLFhURqwRu5cqVpWLFiiIicvToUSlWrJiIiERG\nRkqFChVk7ty5cvPmTdmzZ48EBgbK/v37RSTpcruJBQcHy6xZs0RE5MiRI7JhwwaJioqS8+fPS7Nm\nzWT48OHxx01LTElJXH63SpUqsnHjRhERCQkJkT59+mTk1N7C078LKvvs3ClStWrCcZPatUX27k16\n+ytRV9wboI3QMZIsEhJi3ZSe+JVctk5q+wxmdhGr1G6xYsVo2rQpwcHBjBkzhsWLF9OhQwdatGiB\nr68vI0eO5Nq1a2zdupWqVasSEBDAnj17+P7772nTpg3lypXj4MGDhIWFxY8vrFq1Kr5Ur4+PD/fe\ney9du3ZN0CtJqdxuYtWqVaNFixbxpXFHjBhBWJhVETmtMWXk/FjfdaUy7oEHrClVHn/c2bZ/v9U+\nY8atRekGrBjAmA1j9LuXBl43+2+GhYSkLxGkd/sUJFdq948//qBSpUoJtqtYsSJnzpwBICgoiNDQ\nUI4cOUJQUBBFixYlLCyMbdu2ERQUBMCJEyfYsWMHxYoVi99PTEwMTz75ZPw+Uyq3m9i5c+cYNmwY\nP/zwAxEREcTGxsaXx01rTErZpUgR66n3Vq2sORmvXYPr1+HZZ63B+U8/haJFrW0/bPch7b9sz5d7\nv6T33b3tDdzDaY/Eg5UrV44TcQWpcZbRjat2GBQUxKZNm9i8eTPBwcHxP+JhYWHxP9qVKlUiKCiI\nixcvxr8iIiL4+OOPMxTTSy+9hK+vL/v27ePSpUvMmzcvwQB9WmJKLy1QpbKSMdY8jD/9ZNV8j7N0\nKdx7L2zfbi0HFghkU99N9LwrDbVMcjmvSyQ5fbDdVffu3Vm9ejXfffcd0dHRvP322+TLl49GjkmE\n4n60r1+/Trly5WjSpAlr164lPDw8flC6Q4cOHDp0iPnz5xMdHU10dDQ//vhj/KB9ervtkZGRFCxY\nkMKFC3PmzBneeuutBOvTElN6lSlThuPHj+slBpWlateGHTtg0CBn24kT1i3Cb7wBsbFQME9Br76b\nK8eU2nW3nFpqNyk1a9Zk/vz5DBkyhJIlS7J69WpWrlyJn+P2kxo1ahAQEEDTpk0BKFy4MNWqVaNx\n48bxf8UXKlSI9evXs2jRIsqXL0/ZsmUZM2YMUVFRQPqfEZk4cSK7d++mSJEidOzYkW7duiX4fFpi\nSkpK6x577DEASpQoQb169dIcq1KpyZ/fqrK4dKl12QsgJsYqQ9K2LZw7Z2982U1L7SZB59pSqdHv\ngkrO8ePwxBOwbZuzrXRpa66uVq1sC8stdK4tpZTKAlWqWCVIxoxxFsc6d86qwDhmDERH2xqeR9Me\nicpV9Lug0uLbb62aVnGXtgIC4JdfrGTjjbRHopRSWaxVK2t6lbh68DNnem8SyQraI1G5in4XVHrE\nxlqFs1zn6/JG2iNJxJtu/1VK2cvHx7uTiNZsT4L2SFRq9Lug1K20R6KUUspWmkiUUkpliiYS5XbB\nwcHMmjUr2fX9+/enePHiPPjgg/zwww/UqlXLjdEppdJLE4kHiCvilFukNC3L5s2b2bBhA2fPnmX7\n9u00adIkfl4wsM7Vd999565QlVJpoInEA7ijJnpGubsWyIkTJ6hSpQr58uVLcr0OlivleTSReLAb\nN24wfPhwypcvT/ny5RkxYkT8ZIsAb775JuXKlaNChQp89tln+Pj4cOzYMcAqoft///d/dOjQgcKF\nC/Pggw/GrwPYunUrDzzwAEWLFqV+/fpsc5lgKDg4mHHjxtG4cWMKFSrEsWPH8PHxYfr06dSoUYPC\nhQszYcIEjh49SsOGDSlatCg9evQg2jGHxD///EOHDh0oVaoUxYsXp2PHjvE1VFIya9YsBg4cyLZt\n2wgICGDSpEmEhoZSsWJFAPr06cPJkyfp2LEjAQEBTJ06NUvOs1IqkzJTXtHTXuTgUrtxZWVdjR8/\nXho2bCjnz5+X8+fPS6NGjWT8+PEiIrJmzRopU6aM7N+/X65evSq9evVKUK62b9++UqJECfnxxx8l\nJiZGevXqJT169BARkQsXLkjRokVl/vz5cvPmTVm4cKEUK1ZMwsPDRUQkKChIKleuLPv375ebN29K\nVFSUGGOkc+fOEhERIb/++qvkyZNHmjdvLr///rtcunRJateuLZ9//nn8/r/++mu5du2aREREyGOP\nPSadO3eO/3e5lu5NbO7cudKkSZP45U2bNkmFChVSPVdp5enfBaXsgJbazRohoSGYSeaWV0hoSJq3\nT27bjFqwYAETJkwgMDCQwMBAJk6cyLx58wBYsmQJTz31FHfccQf58+dn0qRJCT5rjKFr167Uq1cP\nX19fevXqxc8//wzA6tWruf322+nVqxc+Pj706NGDWrVqsWLFivjP9uvXjzvuuAMfHx/8/f0BGDVq\nFIUKFaJ27drUqVOHdu3aUaVKFQoXLky7du3Ys2cPAMWLF6dLly7ky5ePQoUK8dJLL8WX402N6GUr\npXIcryu1G1ePJL01SUKCQwgJDsm27TPi7NmzVK5cOX65UqVKnD17FrDK8NavXz9+XVLlckuXLh3/\nPn/+/ERGRsbv17WEL0DlypXj9w3EX05KaX+Jl//8808Arl69yogRI1i3bh0XL14ErIJYIuKxY0FK\n5UahoaFZMhOI1/VIvKmwVbly5Th+/Hj88smTJ+PL7JYtW5ZTp07Fr3N9n5ry5csnKOEL1iB33L4h\nc+Vt3377bQ4dOsTOnTu5dOkSYWFhWTZor4lIqayTVYWtvC6R5FRRUVFcv349/hUTE0PPnj2ZPHky\nf//9N3///Tcvv/wyvXv3BqwyvHPmzOHAgQNcvXqVV155JcH+UvrRbteuHYcOHWLhwoXExMSwePFi\nDhw4QIcOHdL0+aS2cX0fGRlJ/vz5KVKkCOHh4bdcdkvr/pNSunRpjh49mqHPKqWyhyYSD9G+fXsK\nFCgQ/3r55ZcZN24c9erV4+677+buu++mXr16jBs3DoC2bdsydOhQmjdvTs2aNWnYsCEAefPmBZK+\npThuuUSJEqxatYq3336bwMBApk6dyqpVqyhevPgt2ya3nLjN9XjDhw/n2rVrBAYG0qhRI9q1a5em\n/aUWN8CYMWOYPHkyxYoV45133klyH0op99JJG73Eb7/9Rp06dYiKisLHR/8+SE5u+C4olV46aWMu\ntmzZMm7cuMHFixd58cUXeeSRRzSJKKXcTn91crCZM2dSunRpqlevjr+/P9OnT7c7JKVULqSXtlSu\not8FpW6ll7aUUkrZShOJUkqpTNFEopRSKlO8boqU5OgT0UoplT08OpEYYwoCoUCIiKzO6H50cFUp\npbKPp1/aGgUstjuInCgrJmLzFnounPRcOOm5yDrZnkiMMbONMeeMMXsTtbc1xhwwxhw2xryYxOda\nAfuB89kdozfS/0ic9Fw46blw0nORddzRI5kDtHVtMMb4Ah852msDPY0xdxhj+hhj3jXGlAOCgAeB\nJ4CBxqZBjvR82dKybXLbpLU9peXs/g9Dz0Xyx87stuk5F2lp03OR9HJ2nov07tubzkW2JxIR2Qxc\nTNRcHzgiIsdFJBpYBHQSkXkiMkJEzorIOBEZASwAZib5pKEb6I9n8sfO7LZ6LlLfxtN+MJKi5yJj\n+/amc+GWJ9uNMVWAlSJSx7H8KNBGRAY6lnsDDURkSCaPo6PqSimVAZl5st2uu7ay5Qc/MydCKaVU\nxth119YZwLWWa0XgtE2xKKWUygS7EslPQA1jTBVjTB7gcWCFTbEopZTKBHfc/rsQ2ArUNMacMsb0\nF5EYYDCwDusW38Ui8lt2x6KUUirredU08koppdzP059sV0op5eE0kSillMoUTSRKKaUyRROJUkqp\nTNFEopRSKlO8OpEYYwoaYz43xsw0xjxhdzx2MsbcZoz5zBjzld2x2M0Y08nxnVjkmGU61zLG1DLG\nTDfGLDHGDLA7Hrs5fjN+NMY8bHcsdjLGBBtjNju+G0Gpbe/ViQToCiwRkWeAR+wOxk4i8ruIPG13\nHJ5ARJY7vhPPYj0Mm2uJyAERGQT0ANrYHY8H0BpIllggAshLGmYdyXGJJJ31TcoDpxzvb7o1UDfI\naK0Xb5TBczEOq5yBV0nvuTDGdARWY83C7VXScy68vQZSOr8Xm0WkPTAamJTqzkUkR72ApkBdYK9L\nmy9wBKgC+AM/A3cAvYGHHdsstDt2O8+Fy/qv7I7b7nMBGOANoIXdcdt9LhJ9brndsdv8vZgMvIs1\n48Z/cTyw7S2vDP5e5EnLb4ZH12xPiohsdkxL7yq+vgmAMWYR0An4APjIcb3T6+bySs+5MMacA14F\n7jXGvCgib7gz1uyWzu9FS6AFUNgYU11EZrgx1GyXzu9FKaxLwPmATW4M0y3Scy5EZJxjuS9wXhy/\npN4ind+LWliXOosCH6a27xyXSJLhegkLrGt6DUTkKvCUPSHZJrlzEY41JpCbJHcuhpCG/zi8THLn\nIgwIsyck2yR5LuIWRORzt0dkn+S+F68Dy9K6kxw3RpIMr/rLIZP0XDjpuXDSc+Gk58IpS86FtyQS\nrW/ipOfCSc+Fk54LJz0XTllyLrwlkWh9Eyc9F056Lpz0XDjpuXDKknOR4xKJ1jdx0nPhpOfCSc+F\nk54Lp+w8F1qPRCmlVKbkuB6JUkopz6KJRCmlVKZoIlFKKZUpmkiUUkpliiYSpZRSmaKJRCmlVKZo\nIlFKKZUpmkiU1zDGvGuMGeayvM4Y86nL8tvGmBEZ3HewMWZlMu2XjDF7HK/1GYteqZxLE4nyJj8A\njQCMMT5ACaC2y/qGwJa07Mjx+bQKE5G6jlfrRPvxlhm2lUqWJhLlTbZhJQuAO4F9QIQxpqgxJi9W\n8aLdxpgWxpjdxphfjDGzHHMMYYw5box53RizC3jMUTnuN8dylxSOaxIsGNPPGLPCGLMR+NYYU8BR\nnW6H47iPOLbLb6y68fuNMV8bY7YbY+5zrIt02d+jxpg5jvcljTFLjTE7Ha+4xBniOMYmY8xRY8wQ\nl88/aYz5nzHmZ2PM58aYQsaYY3FJzhhT2LHsm/FTr3Iz/WtJeQ0ROWuMiTHGVMRKKNuw6i00BC4D\nv2BVhJsDPCQiR4wxnwODgPexptT+W0TuN8bkAw4BzUXkqDFmMclPud3UGLPH8f4rrBlV6wJ1ROQf\nY8yrwEYRecoYUxTYYYzZgFUfJlJEahtj6gC7Xf85ybx/H3hXRLYYYyoBa3H2umoCzYHCwEFjzDSg\nFjAWaCgi4caYoiISaYwJBR4GlmPVa/+PiHhdOWrlHtojUd5mK9blrUZYiWSb433cZa3bgd9F5Ihj\n+8+BZi6fX+z431qO7Y46lueTqOfhYrPLpa1XHW3fisg/jvetgdGOZLMJyAtUwip9Oh9ARPZiJbrU\ntMSq+rkHKwkEGGMKYiWb1SISLSIXgL+AMsBDwBJHYTNcYvoM6O943w8ruSqVIdojUd5mC9AYqAPs\nxar+NhK4BMxOYntDwr/4rySz3+SSSHIS76eriBxOsENjUtqva0z5E8XRQESiktiXa9tNrP++Jalj\niMhWx9ThwYCviOxP9l+iVCq0R6K8zVagA3BBLBex6k43dKw7BFQxxlRzbN+HpEvNHnBsV9Wx3DMd\nMST+4V4HDI1faUxdx9vvgSccbXcBd7t85pwxppZj0L8LzsSyPtG+7kkhDgG+wxrvKe7YvrjL+i+A\nL0k6wSqVZppIlLfZh3W31naXtl+Af0QkXESuY13S+coY8wsQA3zi2C6+F+DY7hlgtWOw/RxJj5FI\nEu2J214B/B2D+/uASY726UAhY8x+R9sul8+MBlZh9bDOurQPBeo5Bs9/Bf6V6LgJA7F6GlOAMGPM\nz8BUl9ULgGLAwiT+XUqlmdYjUcpDGGM2Af8Wkd2pbpw1x3sU6Cgifd1xPOW9dIxEqVzIGPMh0AZo\nb3csKufTHolSSqlM0TESpZRSmaKJRCmlVKZoIlFKKZUpmkiUUkpliiYSpZRSmfL/vaE/BAtFbMAA\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11e59f0b8>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Creating Simulated Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(empirical_data)\n",
      "simulated_data = fit.power_law.generate_random(10000)\n",
      "\n",
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "####\n",
      "fit = powerlaw.Fit(simulated_data)\n",
      "fit.power_law.xmin, fit.power_law.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "(5.0643668837801314, 2.5102907771973468)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "powerlaw.plot_pdf(simulated_data,linewidth=3)\n",
      "fit.power_law.plot_pdf(simulated_data,linestyle='--',color='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x11e70bb70>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A3YALgN8Bg5xzG4Pe4z3nXMcQPkstAzmiHTu8vYw+/WgP73IVpKRw0vwJNGlW0e/QRHwT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\nICIiwP8HMPOfDwN5UZMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11e6b5048>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "#Advanced Considerations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Discrete Distribution Calculation and Estimation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=True)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=False)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, xmin=230.0, xmax=9000, discrete_approximation='xmax')\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation=100000, xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation='round', xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "0.39905257607692346"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True)\n",
      "simulated_data = theoretical_distribution.generate_random(10000, estimate_discrete=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "theoretical_distributionibution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True, estimate_discrete=False)\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "\n",
      "fit = powerlaw.Fit(empirical_data, discrete=True, estimate_discrete=True)\n",
      "simulated_data = fit.power_law.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Nested Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')\n",
      "fit.distribution_compare('exponential', 'stretched_exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "(-13.018342321459192, 3.3499122220614908e-07)"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Restricted Parameter Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin\n",
      "\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "(1.7831398653341153, 0.063521030949327095, 50.0)"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = {'alpha': [2.3, None], 'sigma': [None, .2]}\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/jeff/Desktop/powerlaw/powerlaw.py:687: RuntimeWarning: overflow encountered in double_scalars\n",
        "  )[1:]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "(2.3000107113942141, 0.17069976919260452, 234.0)"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = lambda self: self.sigma/self.alpha < .05\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "(1.8833765811180314, 0.094168259953067143, 124.0)"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Multiple Possible Fits"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "### Figure 5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "print(fit.xmin, fit.D, fit.alpha)\n",
      "fit = powerlaw.Fit(data)\n",
      "print(fit.xmin, fit.D, fit.alpha)\n",
      "####\n",
      "from matplotlib.pylab import plot\n",
      "plot(fit.xmins, fit.Ds, label=r'$D$')\n",
      "plot(fit.xmins, fit.sigmas, label=r'$\\sigma$', linestyle='--')\n",
      "plot(fit.xmins, fit.sigmas/fit.alphas, label=r'$\\sigma /\\alpha$', linestyle='--')\n",
      "####\n",
      "ylim(0, .4)\n",
      "legend(loc=4)\n",
      "xlabel(r'$x_{min}$')\n",
      "ylabel(r'$D,\\sigma,\\alpha$')\n",
      "\n",
      "figname = 'FigD'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "50.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0998297854528 1.78313986533\n",
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0606737962944 2.27263721983\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mpJaMqk4UkXnA5biO+TdCODZHRG4GpuBGiw1X1YUi0j/w/KvAA4HXfSVw6yhb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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11cf64ac8>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## No Possible Fits"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.001)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin, fit.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "No valid fits found."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "(2.2726372198302882, 0.16568325372336856, 230.0, True)"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit.lognormal.mu, fit.lognormal.sigma\n",
      "range_dict = {'mu': [10.5, None]}\n",
      "fit.lognormal.parameter_range(range_dict)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag\n",
      "\n",
      "initial_parameters = (12, .7)\n",
      "fit.lognormal.parameter_range(range_dict, initial_parameters)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "No valid fits found.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "(10.500000000422041, 5.1423189016918585, False)"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "## Selecting x<sub>min</sub> with Other Distance Metrics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin_distance='D')\n",
      "print(fit.xmin, fit.power_law.alpha, fit.D)\n",
      "fit = powerlaw.Fit(data, xmin_distance='V')\n",
      "print(fit.xmin, fit.power_law.alpha, fit.V)\n",
      "fit = powerlaw.Fit(data, xmin_distance='Asquare')\n",
      "print(fit.xmin, fit.power_law.alpha, fit.Asquare)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.27263721983 0.0606737962944\n",
        "Calculating best minimal value for power law fit\n",
        "219.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.21822784881 0.0921084614746\n",
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.27263721983 0.265613512591\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "variables": {}
     },
     "source": [
      "# Supporting Information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import logspace\n",
      "from scipy.stats import variation\n",
      "import pandas as pd\n",
      "\n",
      "def validate(xmin, alpha, discrete='continuous', n_data=10000, n_trials=1):\n",
      "    \n",
      "    if n_trials>1:\n",
      "        return array([validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=1) for trial in arange(n_trials)]).T\n",
      "        \n",
      "    if discrete=='continuous':\n",
      "        discrete = False\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete':\n",
      "        discrete = True\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete_estimate':\n",
      "        discrete = True\n",
      "        estimate_discrete = True\n",
      "\n",
      "    theoretical_distribution = powerlaw.Power_Law(xmin=xmin, parameters=[alpha], discrete=discrete)\n",
      "    simulated_data = theoretical_distribution.generate_random(n_data, estimate_discrete=estimate_discrete)\n",
      "    fit = powerlaw.Fit(simulated_data, discrete=discrete, estimate_discrete=estimate_discrete)\n",
      "    return fit.xmin, fit.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_trials = 10\n",
      "n_data = 10000\n",
      "theoretical_xmins = unique(floor(logspace(0.0,2.0,num=20)))\n",
      "theoretical_alphas = array([1.5,2.0,2.5,3.0,3.5])\n",
      "distribution_types = ['continuous','discrete']\n",
      "\n",
      "filename = 'powerlaw_validation_%itrials_%idata.csv'%(int(n_trials),int(n_data))\n",
      "\n",
      "from os import listdir\n",
      "files = listdir('.')\n",
      "if filename in files:\n",
      "    print(\"Reading previously calculated data from file %s\"%filename)\n",
      "    df = pd.read_csv(filename)\n",
      "    df.set_index(['type', 'alpha', 'xmin'], inplace=True)\n",
      "else:\n",
      "\n",
      "    ind = [(d,a,x) for d in distribution_types for a in theoretical_alphas for x in theoretical_xmins]\n",
      "    \n",
      "    print(\"Calculating validation fits on %i parameter conditions, with %i trials for each conditions, with %i data points each. \"\n",
      "      \"Could take a long time.\"%(len(ind), n_trials, n_data))\n",
      "\n",
      "    ind = pd.MultiIndex.from_tuples(ind, names=['type', 'alpha','xmin'])\n",
      "    df = pd.DataFrame(columns=['alpha_mean', 'alpha_sd', 'xmin_mean', 'xmin_sd'], index=ind)\n",
      "    \n",
      "    i = 0\n",
      "    for dt, alpha, xmin in ind:\n",
      "        i += 1\n",
      "        print(\"Parameter condition number %i\"%i)\n",
      "        data = validate(xmin, alpha, discrete=dt, n_data=n_data, n_trials=n_trials)\n",
      "        df.ix[dt,alpha,xmin] = (mean(data[1]), std(data[1]), mean(data[0]), std(data[0]))\n",
      "\n",
      "    df.to_csv(filename)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reading previously calculated data from file powerlaw_validation_10trials_10000data.csv\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subplot(2,2,1)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['alpha_mean'].astype('float')\n",
      "    error = df.ix['continuous', a]['alpha_sd'].astype('float')\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "ylabel(r\"Fitted $\\alpha$\")\n",
      "yticks(theoretical_alphas)\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "title(\"Continuous\")\n",
      "\n",
      "#########\n",
      "subplot(2,2,2)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['alpha_mean'].astype('float')\n",
      "    error = df.ix['discrete', a]['alpha_sd'].astype('float')\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "#ylabel(r\"Fitted $\\alpha$\")\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "title(\"Discrete\")\n",
      "\n",
      "########\n",
      "subplot(2,2,3)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['xmin_mean'].astype('float').values\n",
      "    error = df.ix['continuous', a]['xmin_sd'].astype('float').values\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "    \n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "ylabel(r\"Fitted $x_{min}$\")\n",
      "\n",
      "\n",
      "########\n",
      "legend_refs = []\n",
      "########\n",
      "subplot(2,2,4,sharey=gca())\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['xmin_mean'].astype('float').values\n",
      "    error = df.ix['discrete', a]['xmin_sd'].astype('float').values\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "\n",
      "    line = plot(theoretical_xmins, y_vals, label=a)\n",
      "    legend_refs += line\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "#ylabel(r\"Fitted $x_{min}$\")\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "\n",
      "\n",
      "#######\n",
      "#figlegend(legend_refs[::-1], theoretical_alphas[::-1],'center right', title=r'$\\alpha$ of Data')\n",
      "subplots_adjust(wspace=.15, hspace=.1)\n",
      "legend( legend_refs[::-1], theoretical_alphas[::-1], loc = 'center right', bbox_to_anchor = (.1,0,1,1),\n",
      "            bbox_transform = plt.gcf().transFigure, title=r'$\\alpha$ of Data' )\n",
      "savefig('Fig_powerlaw_validation_%itrials_%idata.pdf'%(int(n_trials),int(n_data)), bbox_inches='tight')\n",
      "savefig('Fig_powerlaw_validation_%itrials_%idata.tiff'%(int(n_trials),int(n_data)), bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GWzEax/4eksT7gxAtFpFyKZMjf+1cloiizDay4FKHjozC7t2wewgZ2o0MDyND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       "text": [
        "<matplotlib.figure.Figure at 0x108384a58>"
       ]
      }
     ],
     "prompt_number": 45
    }
   ],
   "metadata": {}
  }
 ]
}